Description: An alternate definition
of double existential uniqueness (see 2eu42227).
A mistake sometimes made in the literature is to use to
mean "exactly one and exactly one ." (For example, see
Proposition 7.53 of [TakeutiZaring] p. 53.) It turns out that
this is
actually a weaker assertion, as can be seen by expanding out the formal
definitions. This theorem shows that the erroneous definition can be
repaired by conjoining as an additional condition. The
correct definition apparently has never been published. ( means
"exists at most one.") (Contributed by NM,
26-Oct-2003.)